Is there a quick way to snap an object's origin to world origin along a specific axis?
If you want to snap the object's origin to the world origin (0,0,0) all at once, there's the shortcut Alt+G (clear location).

If you want to snap it to just one axis at a time, you can do this by:


Checking the "Manipulate center points" to transform the origin only (and not the entire object).
Changing the pivot point to 3D cursor.
Snapping the cursor to the world origin (Shift+C).
Scaling any axis to 0 to snap the object origin to that axis:
For instance, SX0 Snaps your object to the X axis.


See animation below for a demonstration of the method: